Problem: $A=\left[\begin{array}{rr}-14 & 4 & -4 & 3 & 16 \\2 & 8 & 19 & 5 & 7 \\3 &0 & 9 & 2 & 8 \\-6 &-4 &-13 & 3 & 1 \\0 &-1 &12 & 0 & 7\end{array}\right]$ $A_{5,4}=$
Solution: Background An $m\times n$ matrix has $m$ rows and $n$ columns. $A=\left[\begin{array}{rr}A_{1,1} & \cdots & A_{1,n} \\\\\vdots \ & \ddots & \vdots \\\\A_{m,1} &\cdots &A_{m,n}\end{array}\right]$ Therefore, the entry $A_{{c},{d}}$ is located on row ${c}$ and column ${d}$. Finding $A_{5,4}$ $A_{{5},{4}}$ is located on row ${5}$ of $A$ : $\left[\begin{array}{rr}-14 & 4 & -4 & 3 & 16 \\2 & 8 & 19 & 5 & 7 \\3 &0 & 9 & 2 & 8 \\-6 &-4 &-13 & 3 & 1 \\ {0} & {-1} & {12} & {0} & {7}\end{array}\right]$ $A_{{5},{4}}$ is also located on column ${4}$ of $A$. $\left[\begin{array}{rr}-14 & 4 & -4 & 3 & 16 \\2 & 8 & 19 & 5 & 7 \\3 &0 & 9 & 2 & 8 \\-6 &-4 &-13 & 3 & 1 \\ {0} & {-1} & {12} & {\text0} & {7}\end{array}\right]$ Therefore, $A_{{5},{4}}={0}$. Summary $A_{5,4}=0$